Multiple scattering : interaction of time-harmonic waves with N obstacles / P. A. Martin.

Format:

Book

Author/Creator:

Martin, P. A., author.

Series:

Encyclopedia of mathematics and its applications ; v. 107.

Encyclopedia of mathematics and its applications ; volume 107

Language:

English

Subjects (All):

Multiple scattering (Physics).

Physical Description:

1 online resource (xii, 437 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2006.

Language Note:

English

Summary:

The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

Contents:

Cover; Title; Copyright; Dedication; Contents; Preface; 1 Introduction; 1.1 What is 'multiple scattering'?; 1.1.1 Single scattering and independent scattering; 1.1.1.1 Single scattering; 1.1.1.2 Independent scattering; 1.1.2 Scattering by N obstacles; 1.1.3 Self-consistent methods; 1.1.4 Rayleigh's paper of 1892; 1.1.5 Kasterin, KKR and the electronic structure of solids; 1.2 Narrowing the scope: previous reviews and omissions; 1.3 Acoustic scattering by N obstacles; 1.3.1 The Sommerfeld radiation condition; 1.3.2 Boundary conditions; 1.3.3 Transmission problems; 1.3.4 Inhomogeneous obstacles

1.4 Multiple scattering of electromagnetic waves1.4.1 The Silver-Müller radiation conditions; 1.4.2 Boundary condit; 1.4.3 Transmission problems; 1.4.4 Inhomogeneous obstacles; 1.5 Multiple scattering of elastic waves; 1.5.1 The Kupradze radiation condit; 1.5.2 Boundary conditions; 1.5.3 Transmission problems; 1.5.4 Inhomogeneous obstacles; 1.5.5 Two-dimensional problems; 1.5.6 Half-space problems; 1.6 Multiple scattering of water waves; 1.6.1 Boundary conditions; 1.6.2 Radiation conditions; 1.6.3 Two-dimensional problems; 1.6.4 Vertical cylinders; 1.6.5 Uniqueness; 1.7 Overview of the book

2 Addition theorems in two dimensions2.1 Introduction; 2.2 Cartesian coordinates; 2.3 Hobson's theorem; 2.4 Wavefunctions; 2.5 Addition theorems; 2.6 The separation matrices S and S; 2.7 Use of rotation matrices; 2.8 Two-centre expansions; 2.9 Elliptical wavefunctions; 2.9.1 Addition theorems; 2.10 Vector cylindrical wavefunctions; 2.11 Multipoles for water waves; 2.11.1 A fundamental solution for deep water; 2.11.2 Addition theorems; 3 Addition theorems in three dimensions; 3.1 Introduction; 3.2 Spherical harmonics; 3.3 Legendre's addition theorem; 3.4 Cartesian coordinates

3.5 Hobson's theorem3.6 Wavefunctions and the operator m n; 3.7 First derivatives of spherical wavefunctions; 3.8 Axisymmetric addition theorems; 3.9 A useful lemma; 3.10 Composition formula for the operator m n; 3.11 Addition theorem for jnY m n; 3.12 Addition theorem for h 1 n Y m n; 3.13 The separation matrices S and S; 3.13.1 Computation of the separation matrices; 3.13.2 A wide-spacing approximation; 3.13.3 Separable formulae for the separation matrices; 3.14 Two-centre expansions; 3.14.1 Second proof of the addition theorem for h1n Y m; 3.14.2 A formula for S(a+b)

4.6 Separation of variables for one sphere

Notes:

Title from publisher's bibliographic system (viewed on 25 May 2016).

Includes bibliographical references (p. 357-420) and indexes.

ISBN:

1-139-88333-X

1-107-38403-6

1-107-38754-X

0-511-83879-4

0-511-73511-1

1-107-39046-X

1-107-39887-8

1-107-39526-7

OCLC:

776951259